Speeding up the ordered allocation sampler
Existing ordered allocation samplers for posterior inference in nonparametric mixture models suffer from low sampling efficiency and implementation complexity. Method: We propose an improved ordered allocation sampler that integrates a marginalization-based sampling structure, incorporates the Jain–Neal split–merge move strategy, and synergistically combines conditional sampling with class-marginal sampling within a Gibbs framework to accommodate nonexchangeable mixture priors. Contribution/Results: The method significantly enhances sampling efficiency and convergence speed while simplifying algorithmic implementation. Empirical evaluations demonstrate superior posterior exploration capability and computational robustness compared to state-of-the-art approaches, across both infinite mixture models and finite mixtures with random component counts. Theoretical rigor is preserved, and the method exhibits broad practical applicability.